第二届IMACS计算物理会议简讯

第二届ＩＭＡＣＳ计算物理会议简讯第二届ＩＭＡＣＳ（国际数学与计算机模拟）计算物理会议于１９９３年１０月６日至９日在美国Ｓｔ．Ｌｏｕｉｓ（圣路易斯）城召开。会议代表１００多人，宣读论文（包括大会特邀报告与分组会报告）共９５篇。分组会报告分如下专题：（１...     

平面十次对称准晶中Ⅱ型Briffith裂纹的求解

应用应力函数法,求解了二维十次对称准晶中的Ⅱ型Griffith裂纹问题。特别是把二维准晶的弹性力学问题分解成一个平面应变问题与一个反平面问题的叠加,通过引入应力函数,把平面应变问题的十八个弹性力学基本方程简化成一个八阶偏微分方程,并且求出了其在Ⅱ型Griffith裂纹情况的混合边值问题的解,所有的应力分量和位移分量都用初等函数表示出来,并且由此得出了准晶中Ⅱ型Griffith裂纹问题的应力强度因子和能量释放率。     

The stress field and energy of screw dislocation in smectic A liquid crystals and the mistakes of the classical solution

The mistakes in the classical solution of a screw dislocation in smectic A liquid crystals are pointed out. A serious problem with the well-known theory is pointed, which may be named de Gennes-Kleman-Pershan paradox and has existed for many decades in the scientific community of liquid crystal study. The correct solution is given in this paper by a simplest, elementary, and straight forward method. In connection with this, the stress field and energy of dislocation are discussed in detail. The present article provides the correct stress field and dislocation energy as well.     

Interface of quasicrystal and crystal

A model on the coexisting phase of quasicrystal-crystal is proposed,with which we concretely investigate the interface effects for coexisting phases of one-dimensional orthorhombic quasicrystal-isotropic crystal and three-dimensional icosahedral quasicrystal-cubic crystal.The phason strain fields which play an important role in some processes are determined.Some factors affecting the strain fields,e.g.,the material constants of phonon,phason,phonon-phason coupling of the quasicrystal and the elastic modulus and the size of the crystal are also explored.     

Elastic analysis of a mode Ⅱ crack in an icosahedral quasicrystal

Based on the displacement potential functions, the elastic analysis of a mode II crack in an icosahedral quasicrystal is performed by using the Fourier transform and dual integral equation theory. By the solution, the analytic expressions for the displacement field and stress field are obtained. The asymptotic behaviours of the phonon and phason stress fields around the crack tip indicate that the stresses near the crack tip exhibit a square root singularity. The most important physical quantities of fracture theory, crack stress intensity factor and energy release rate, are evaluated in an explicit version.     

A MODE Ⅱ CRACK IN A TWO-DIMENSIONAL OCTAGONAL QUASICRYSTALS

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｄｉｓｃｏｖｅｒｙｏｆｑｕａｓｉｃｒｙｓｔａｌａｒｏｕｎｄ 1 984 [1,2 ,3]ｉｓｓｉｇｎｉｆｉｃａｎｔｂｒｅａｋｔｈｒｏｕｇｈｆｏｒｃｏｎｄｅｎｓｅｄｍａｔｔｅｒｐｈｙｓｉｃｓｉｎｒｅｃｅｎｔｙｅａｒｓ.Ｔｈｅｑｕａｓｉｐｅｒｉｏｄｉｃｓｙｍｍｅｔｒｙｏｆｓｏｌｉｄｐｒｅｓｅｎｔｓｇｒｅａｔｔｈｅｏｒｅｔｉｃａｌｓｉｇｎｉｆｉｃａｎｃｅ .Ｎｕｍｅｒｏｕｓｑｕａｓｉｃｒｙｓｔａｌｌｉｎｅｍａｔｅｒｉａｌｓｗｉｔｈｓｔａｂｌｅｐｒｏｐｅｒｔｙｗｅｒｅｐｒｏｄｕｃｅｄ ,ｔｈｉ…     

立方准晶材料的剪切裂纹问题

通过引入位移函数,使得立方准晶的轴对称弹性问题归结为求解一个高阶偏微分方程.在此基础上,研究了立方准晶含有圆盘状裂纹的剪切问题,得到了此问题弹性场的精确解析解,以及应力强度因子与应变能释放率.     

A class of two-dimensional dual integral equations and its application

Because exact analytic solution is not available,we use double expansion and boundary collocation to construct an approximate solution for a class of two-dimensional dual integral equations in mathematical physics.The integral equations by this procedure are reduced to infinite algebraic equations.The accuracy of the solution lies in the boundary collocation technique.The application of which for some complicated initial- boundary value problems in solid mechanics indicates the method is powerful.     

AXISYMMETRIC ELASTICITY PROBLEM OF CUBIC QUASICRYSTAL

A method for analyzing the elasticity problem of cubic quasicrystal is developed. The axisymmetric elasticity problem of cubic quasicrystal is reduced to a single higher-order partial differential equation by introducing a displacement function. As an example, the solutions of elastic field of cubic quasicrystal with a penny-shaped crack are obtained, and the stress intensity factor and strain energy release rate are determined.     

PERTURBATION METHOD SOLVING ELASTIC PROBLEMS OF ICOSAHEDRAL QUASICRYSTALS CONTAINING A CIRCULAR CRACK

Perturbation method for solving elastic three-dimensional (3D) problems for 3D icosahedral quasicrystals is proposed. Considering an infinite 3D icosahedral quasicrystal weakened by a circular crack, we obtain the uniformly valid asymptotic solutions up to O(R²) for the mode I loading, where R is the elastic constant of phonon-phason coupling.